Crack Propagation Pattern in a Disk of Brittle Material under Axisymmetrical Tension

Crack propagation and branching behavior in a disk under axisymmetrical tension was analyzed by using an energy consideration. The result was compared with the experimental result of flexual test in which a glass or ceramic disk was supported along its edge and load was applied at the center of disk. If crack branching occurs by the decrease of free energy of the system, the crack length ai after the i-th crack branching has occurred is given as follows: ai≈22i+1/(2i+1-1)·Eγ/πσ2 Where E is elastic modulus, γ is surface energy, σ is tensile stress, and n=2i+1 is number of cracks. The surface energy γ, which was calculated by dividing the stored strain energy in a disk before fracture by the total crack surface, was almost the same independently of the number of cracks. The crack branching pattern observed for disk specimens agreed relatively well with the pattern calculated from the above equation.